Theorems · Theorem · linear algebra
Module.card_fintype
∀ {ι : Type u_1} {R : Type u_3} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[inst_3 : Fintype ι] (b : Module.Basis ι R M) [inst : Fintype R] [inst_4 : Fintype M],
Fintype.card M = Fintype.card R ^ Fintype.card ι- Defined in
- Mathlib.LinearAlgebra.Basis.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Fintypestatement and proof · cited by 7,736
- Module.Basisstatement and proof · cited by 1,477
- Fintype.cardstatement and proof · cited by 1,386
- Finset.prod_constproof · cited by 154
- LinearEquiv.toEquivproof · cited by 105
- Module.Basis.equivFunproof · cited by 88
- Fintype.card_congrproof · cited by 67
- Fintype.card_piproof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- Module.card_eq_pow_finrankproof · cited by 4
- GaloisField.cardproof · cited by 1
- VectorSpace.card_fintypeproof · cited by 1